Collective modes of a trapped strongly interacting

Fermi gas near the unitary limit regime

陆振帮

华中师范大学粒子物理研究所 (IOPP, CCNU)武汉科技学院理学院 (WUSE)

合肥 2009

OUTLINE

1. Background

2. Equation of state

3. Collective modes

4. Summary

Background

Unitary limit a 24 / k

Universality

BCS-BEC crossover

Feshbach resonance

Background

Collective behaviorHydrodynamics

Breathing modes

Exp. data 6 Li

Strongly interacting many-body problem

Ground state energy 0.42 0.46 Equation of state (EOS)

Equation of state

Hamiltonian

Zero temperature ground state energy

Equation of state

1fk ax

Collective modes

Hydrodynamic equations

Equation of continuity

Euler equation

Collective modes

Polytropic EOS

1P Cn

2

3

1

Dilute gas of Fermi atoms in both hydrodynamic and superfluid limits

Fermi gas and BEC in unitary limit

Dilute interaction dominated BEC

Collective modes

ln( ) 1

ln

d Px

d n

Collective modes

Linearization eqn n n v n

Considering the breathing modes i ti i iia re ev

Collective modes

Equantions for ( 1,2,3)ia i

2 2 2( 2 )i i i jj

a a

In an axial symmetric trap

rad 1,2 0

ax 3 0

where is the anisotropy parameter.

Collective modes

± signs correspond to the radial and axial modes respectively.

purely geometric, irrelevant to EOS.

In a cigar-shaped trap as being equipped in the experiments whose data are now available

The radial modes:

The axial modes:

rad rad2( 1)

ax ax

3 2

1

1

Collective modes

The radial breathing modes compared with experimental data.

Collective modes

The axial breathing modes compared with experimental data.

Collective modes

Summary

With the proposed equation of state, we have analyzed the hydrodynamic modes. For Fermi gas in a cigar-shaped harmonic trap potential, the radial and axial breathing mode frequencies are derived. The results are in agreement with the experimental measurements.

Thank you!